**Problem 3:** A 1.20 kg solid ball of radius 40 cm rolls down a 5.20 m long incline of 25 degrees. Ignoring any loss due to friction, how fast will the ball be rolling when it reaches the bottom of the incline?---**Explanation:**This problem involves calculating the speed of a rolling solid ball as it descends an inclined plane. By assuming no energy loss due to friction or air resistance, you can use the conservation of energy principle to find the final speed of the ball at the bottom of the incline.**Key Concepts:**- **Conservation of Energy:** - Potential Energy (PE) at the top is converted into Kinetic Energy (KE) at the bottom. - PE = mgh, where m is mass, g is acceleration due to gravity, and h is the height of the incline. - KE = \( \frac{1}{2} mv^2 + \frac{1}{2} Iω^2 \), where v is linear velocity, I is the moment of inertia, and ω is angular velocity.- **Moment of Inertia for a Solid Sphere:** - \( I = \frac{2}{5} mr^2 \).- **Relation between linear velocity (v) and angular velocity (ω):** - \( v = rω \).**Steps:**1. **Calculate the height (h) of the incline:** - \( h = 5.20 \, m \times \sin(25^\circ) \).2. **Apply energy conservation:** - Initial Potential Energy = Total Kinetic Energy at the bottom. - \( mgh = \frac{1}{2} mv^2 + \frac{1}{2} \left(\frac{2}{5} mr^2\right) \left(\frac{v}{r}\right)^2 \).3. **Solve for v (final velocity):**Through this process, you can determine how fast the ball will be rolling when it reaches the bottom of the incline.

mass, m = 1.2 kg radius, r =40 cm length, L =5.2 m Angle, A = 25 degree

3. A 1.20 kg solid ball of radius 40 cm rolls down a 5.20 m long incline of 25 degrees. Ignoring any loss due to friction, how fast will the ball be rolling when it reaches the bottom of the incline? |

3. A 1.20 kg solid ball of radius 40 cm rolls down a 5.20 m long incline of 25 degrees. Ignoring any loss due to friction, how fast will the ball be rolling when it reaches the bottom of the incline? |

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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